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Paradoxes in Mathematics (Dover Books on Mathematics)
by Stanley J. FarlowThere's more than one way to define a paradox, and this intriguing book offers examples of every kind. Stanley J. Farlow, a prominent educator and author, presents a captivating mix of mathematical paradoxes: the kind with surprising, nonintuitive outcomes; the variety that rely on mathematical sleight-of-hand to impress the unwary observer; and the baffling type with a solution that passes all understanding.Students and puzzle enthusiasts will find plenty of thought-provoking enjoyment mixed with a bit of painless mathematical instruction among these twenty-eight conundrums. Some of them involve counting, some deal with infinity, and others draw on principles of geometry and arithmetic. None requires an extensive background in higher mathematics. Challenges include The Curve That Shook the World, a variation on the famous Monty Hall Problem, Space Travel in a Wineglass, Through Cantor's Looking Glass, and other fun-to-ponder paradoxes.
Paradoxes in Probability Theory
by William EckhardtParadoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.
Paradoxes of the Infinite (Routledge Revivals)
by Bernard BolzanoParadoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19th century: Dr Bernard Bolzano’s Paradoxien. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.
Parallel Algorithms in Computational Science and Engineering (Modeling and Simulation in Science, Engineering and Technology)
by Ananth Grama Ahmed H. SamehThis contributed volume highlights two areas of fundamental interest in high-performance computing: core algorithms for important kernels and computationally demanding applications. The first few chapters explore algorithms, numerical techniques, and their parallel formulations for a variety of kernels that arise in applications. The rest of the volume focuses on state-of-the-art applications from diverse domains. By structuring the volume around these two areas, it presents a comprehensive view of the application landscape for high-performance computing, while also enabling readers to develop new applications using the kernels. Readers will learn how to choose the most suitable parallel algorithms for any given application, ensuring that theory and practicality are clearly connected. Applications using these techniques are illustrated in detail, including:Computational materials science and engineeringComputational cardiovascular analysisMultiscale analysis of wind turbines and turbomachineryWeather forecastingMachine learning techniquesParallel Algorithms in Computational Science and Engineering will be an ideal reference for applied mathematicians, engineers, computer scientists, and other researchers who utilize high-performance computing in their work.
Parallel Computers 2: Architecture, Programming and Algorithms
by R.W Hockney C.R JesshopeSince the publication of the first edition, parallel computing technology has gained considerable momentum. A large proportion of this has come from the improvement in VLSI techniques, offering one to two orders of magnitude more devices than previously possible. A second contributing factor in the fast development of the subject is commercialization. The supercomputer is no longer restricted to a few well-established research institutions and large companies. A new computer breed combining the architectural advantages of the supercomputer with the advance of VLSI technology is now available at very attractive prices. A pioneering device in this development is the transputer, a VLSI processor specifically designed to operate in large concurrent systems. Parallel Computers 2: Architecture, Programming and Algorithms reflects the shift in emphasis of parallel computing and tracks the development of supercomputers in the years since the first edition was published. It looks at large-scale parallelism as found in transputer ensembles. This extensively rewritten second edition includes major new sections on the transputer and the OCCAM language. The book contains specific information on the various types of machines available, details of computer architecture and technologies, and descriptions of programming languages and algorithms. Aimed at an advanced undergraduate and postgraduate level, this handbook is also useful for research workers, machine designers, and programmers concerned with parallel computers. In addition, it will serve as a guide for potential parallel computer users, especially in disciplines where large amounts of computer time are regularly used.
Parallel Computing: Methods, Algorithms and Applications
by David J Evans; C SuttiParallel Computing: Methods, Algorithms and Applications presents a collection of original papers presented at the international meeting on parallel processing, methods, algorithms, and applications at Verona, Italy in September 1989.
Parallel Computing Technologies: 17th International Conference, PaCT 2023, Astana, Kazakhstan, August 21–25, 2023, Proceedings (Lecture Notes in Computer Science #14098)
by Victor MalyshkinThis book constitutes the refereed proceedings of the 17th International Conference on Parallel Computing Technologies, PaCT 2023, held in Astana, Kazakhstan, during August 21-25, 2023. The 15 full papers included in this book were carefully reviewed and selected from 23 submissions. They were organized in topical sections as follows: automatic programming and program tuning; frameworks and services; algorithms; and distributed systems management.
Parallel Curriculum Units for Mathematics, Grades 6–12
by Dr Jann H. Leppien Dr Jeanne H. PurcellMaximize your mathematics curriculum to challenge all students This collection of lessons from experienced teachers provides multifaceted examples of rigorous learning opportunities for mathematics students in Grades 6–12. The four sample units focus on fractions, linear programming, geometry, and quadratic relationships. The authors provide user-friendly methods for instruction and demonstrate how to differentiate the lessons for the benefit of all students. Included are standards-based strategies that guide students through: Understanding secondary mathematics concepts Discovering connections between mathematics and other subjects Developing critical thinking skills Connecting mathematics learning to society through the study of real-world data, proportional reasoning, and problem solving
Parallel Finite Volume Computation on General Meshes
by Yuri Vassilevski Kirill Terekhov Kirill Nikitin Ivan KapyrinThis book presents a systematic methodology for the development of parallel multi-physics models and its implementation in geophysical and biomedical applications. The methodology includes conservative discretization methods for partial differential equations on general meshes, as well as data structures and algorithms for organizing parallel simulations on general meshes. The structures and algorithms form the core of the INMOST (Integrated Numerical Modelling Object-oriented Supercomputing Technologies) platform for the development of parallel models on general meshes. The authors consider applications for addressing specific geophysical and biomedical challenges, including radioactive contaminant propagation with subsurface waters, reservoir simulation, and clot formation in blood flows. The book gathers all the components of this methodology, from algorithms and numerical methods to the open-source software, as well as examples of practical applications, in a single source, making it a valuable asset for applied mathematicians, computer scientists, and engineers alike.
Parallel-in-Time Integration Methods: 9th Parallel-in-Time Workshop, June 8–12, 2020 (Springer Proceedings in Mathematics & Statistics #356)
by Benjamin Ong Jacob Schroder Jemma Shipton Stephanie FriedhoffThis volume includes contributions from the 9th Parallel-in-Time (PinT) workshop, an annual gathering devoted to the field of time-parallel methods, aiming to adapt existing computer models to next-generation machines by adding a new dimension of scalability. As the latest supercomputers advance in microprocessing ability, they require new mathematical algorithms in order to fully realize their potential for complex systems. The use of parallel-in-time methods will provide dramatically faster simulations in many important areas, including biomedical (e.g., heart modeling), computational fluid dynamics (e.g., aerodynamics and weather prediction), and machine learning applications. Computational and applied mathematics is crucial to this progress, as it requires advanced methodologies from the theory of partial differential equations in a functional analytic setting, numerical discretization and integration, convergence analyses of iterative methods, and the development and implementation of new parallel algorithms. Therefore, the workshop seeks to bring together an interdisciplinary group of experts across these fields to disseminate cutting-edge research and facilitate discussions on parallel time integration methods.
Parallel Problem Solving from Nature – PPSN XV: 15th International Conference, Coimbra, Portugal, September 8–12, 2018, Proceedings, Part I (Lecture Notes in Computer Science #11101)
by Anne Auger Carlos M. Fonseca Nuno Lourenço Penousal Machado Luís Paquete Darrell WhitleyThis two-volume set LNCS 11101 and 11102 constitutes the refereed proceedings of the 15th International Conference on Parallel Problem Solving from Nature, PPSN 2018, held in Coimbra, Portugal, in September 2018. The 79 revised full papers were carefully reviewed and selected from 205 submissions. The papers cover a wide range of topics in natural computing including evolutionary computation, artificial neural networks, artificial life, swarm intelligence, artificial immune systems, self-organizing systems, emergent behavior, molecular computing, evolutionary robotics, evolvable hardware, parallel implementations and applications to real-world problems. The papers are organized in the following topical sections: numerical optimization; combinatorial optimization; genetic programming; multi-objective optimization; parallel and distributed frameworks; runtime analysis and approximation results; fitness landscape modeling and analysis; algorithm configuration, selection, and benchmarking; machine learning and evolutionary algorithms; and applications. Also included are the descriptions of 23 tutorials and 6 workshops which took place in the framework of PPSN XV.
Parallel Problem Solving from Nature – PPSN XV: 15th International Conference, Coimbra, Portugal, September 8–12, 2018, Proceedings, Part II (Lecture Notes in Computer Science #11102)
by Anne Auger Carlos M. Fonseca Nuno Lourenço Penousal Machado Luís Paquete Darrell WhitleyThis two-volume set LNCS 11101 and 11102 constitutes the refereed proceedings of the 15th International Conference on Parallel Problem Solving from Nature, PPSN 2018, held in Coimbra, Portugal, in September 2018. The 79 revised full papers were carefully reviewed and selected from 205 submissions. The papers cover a wide range of topics in natural computing including evolutionary computation, artificial neural networks, artificial life, swarm intelligence, artificial immune systems, self-organizing systems, emergent behavior, molecular computing, evolutionary robotics, evolvable hardware, parallel implementations and applications to real-world problems. The papers are organized in the following topical sections: numerical optimization; combinatorial optimization; genetic programming; multi-objective optimization; parallel and distributed frameworks; runtime analysis and approximation results; fitness landscape modeling and analysis; algorithm configuration, selection, and benchmarking; machine learning and evolutionary algorithms; and applications. Also included are the descriptions of 23 tutorials and 6 workshops which took place in the framework of PPSN XV.
Parallel Problem Solving from Nature – PPSN XVI: 16th International Conference, PPSN 2020, Leiden, The Netherlands, September 5-9, 2020, Proceedings, Part II (Lecture Notes in Computer Science #12270)
by Thomas Bäck Mike Preuss André Deutz Hao Wang Carola Doerr Michael Emmerich Heike TrautmannThis two-volume set LNCS 12269 and LNCS 12270 constitutes the refereed proceedings of the 16th International Conference on Parallel Problem Solving from Nature, PPSN 2020, held in Leiden, The Netherlands, in September 2020. The 99 revised full papers were carefully reviewed and selected from 268 submissions. The topics cover classical subjects such as automated algorithm selection and configuration; Bayesian- and surrogate-assisted optimization; benchmarking and performance measures; combinatorial optimization; connection between nature-inspired optimization and artificial intelligence; genetic and evolutionary algorithms; genetic programming; landscape analysis; multiobjective optimization; real-world applications; reinforcement learning; and theoretical aspects of nature-inspired optimization.
Parallel Problem Solving from Nature – PPSN XVI: 16th International Conference, PPSN 2020, Leiden, The Netherlands, September 5-9, 2020, Proceedings, Part I (Lecture Notes in Computer Science #12269)
by Thomas Bäck Mike Preuss André Deutz Hao Wang Carola Doerr Michael Emmerich Heike TrautmannThis two-volume set LNCS 12269 and LNCS 12270 constitutes the refereed proceedings of the 16th International Conference on Parallel Problem Solving from Nature, PPSN 2020, held in Leiden, The Netherlands, in September 2020. The 99 revised full papers were carefully reviewed and selected from 268 submissions. The topics cover classical subjects such as automated algorithm selection and configuration; Bayesian- and surrogate-assisted optimization; benchmarking and performance measures; combinatorial optimization; connection between nature-inspired optimization and artificial intelligence; genetic and evolutionary algorithms; genetic programming; landscape analysis; multiobjective optimization; real-world applications; reinforcement learning; and theoretical aspects of nature-inspired optimization.
Parallel Problem Solving from Nature – PPSN XVIII: 18th International Conference, PPSN 2024, Hagenberg, Austria, September 14–18, 2024, Proceedings, Part IV (Lecture Notes in Computer Science #15151)
by Michael Affenzeller Stephan M. Winkler Anna V. Kononova Heike Trautmann Tea Tušar Penousal Machado Thomas BäckThis multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024. The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections: Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis. Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization. Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics. Part IV: Multi-Objective Optimization; Real-World Applications.
Parallel Problem Solving from Nature – PPSN XVIII: 18th International Conference, PPSN 2024, Hagenberg, Austria, September 14–18, 2024, Proceedings, Part III (Lecture Notes in Computer Science #15150)
by Thomas Bäck Penousal Machado Heike Trautmann Anna V. Kononova Tea Tušar Michael Affenzeller Stephan M. WinklerThis multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024. The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections: Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis. Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization. Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics. Part IV: Multi-Objective Optimization; Real-World Applications.
Parallel Problem Solving from Nature – PPSN XVIII: 18th International Conference, PPSN 2024, Hagenberg, Austria, September 14–18, 2024, Proceedings, Part I (Lecture Notes in Computer Science #15148)
by Thomas Bäck Penousal Machado Heike Trautmann Anna V. Kononova Tea Tušar Michael Affenzeller Stephan M. WinklerThis multi-volume LNCS set, LNCS 15148-15151, constitutes the refereed proceedings of the 18th International Conference on Parallel Problem Solving from Nature, PPSN 2024, held in Hagenberg, Austria, in September 2024. The 101 full papers presented in these proceedings were carefully reviewed and selected from 294 submissions. The papers presented in these four volumes are organized in the following topical sections: Part I: Combinatorial Optimization; Genetic Programming; Fitness Landscape Modeling and Analysis. Part II: Benchmarking and Performance Measures; Automated Algorithm Selection and Configuration; Numerical Optimization; Bayesian- and Surrogate-Assisted Optimization. Part III: Theoretical Aspects of Nature-Inspired Optimization; (Evolutionary) Machine Learning and Neuroevolution; Evolvable Hardware and Evolutionary Robotics. Part IV: Multi-Objective Optimization; Real-World Applications.
Parallel Processing and Applied Mathematics: 4th International Conference, Ppam 2001, Naleczow, Poland, September 9-12, 2001, Revised Papers (Lecture Notes in Computer Science #2328)
by Konrad Karczewski Ewa Deelman Jack Dongarra Roman WyrzykowskiThe two-volume set LNCS 10777 and 10778 constitutes revised selected papers from the 12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017, held in Lublin, Poland, in September 2017.The 49 regular papers presented in this volume were selected from 98 submissions. For the workshops and special sessions, that were held as integral parts of the PPAM 2017 conference, a total of 51 papers was accepted from 75 submissions. The papers were organized in topical sections named as follows:Part I: numerical algorithms and parallel scientific computing; particle methods in simulations; task-based paradigm of parallel computing; GPU computing; parallel non-numerical algorithms; performance evaluation of parallel algorithms and applications; environments and frameworks for parallel/distributed/cloud computing; applications of parallel computing; soft computing with applications; and special session on parallel matrix factorizations. Part II: workshop on models, algorithms and methodologies for hybrid parallelism in new HPC systems; workshop power and energy aspects of computations (PEAC 2017); workshop on scheduling for parallel computing (SPC 2017); workshop on language-based parallel programming models (WLPP 2017); workshop on PGAS programming; minisymposium on HPC applications in physical sciences; minisymposium on high performance computing interval methods; workshop on complex collective systems.
Parallel Processing and Applied Mathematics
by Kazimierz Wiatr Jacek Kitowski Konrad Karczewski Jack Dongarra Ewa Deelman Roman WyrzykowskiThis two-volume set LNCS 9573 and LNCS 9574 constitutes the refereed proceedings of the 11th International Conference of Parallel Processing and Applied Mathematics, PPAM 2015, held in Krakow, Poland, in September 2015. The 111 revised full papers presented in both volumes were carefully reviewed and selected from 196 submissions. The focus of PPAM 2015 was on models, algorithms, and software tools which facilitate efficient and convenient utilization of modern parallel and distributed computing architectures, as well as on large-scale applications, including big data problems.
Parallel Processing and Applied Mathematics
by Roman Wyrzykowski Jack Dongarra Konrad Karczewski Jerzy WaśniewskiThis two-volume-set (LNCS 8384 and 8385) constitutes the refereed proceedings of the 10th International Conference of Parallel Processing and Applied Mathematics, PPAM 2013, held in Warsaw, Poland, in September 2013. The 143 revised full papers presented in both volumes were carefully reviewed and selected from numerous submissions. The papers cover important fields of parallel/distributed/cloud computing and applied mathematics, such as numerical algorithms and parallel scientific computing; parallel non-numerical algorithms; tools and environments for parallel/distributed/cloud computing; applications of parallel computing; applied mathematics, evolutionary computing and metaheuristics.
Parallel Processing and Applied Mathematics
by Roman Wyrzykowski Jack Dongarra Konrad Karczewski Jerzy WaśniewskiThis two-volume-set (LNCS 8384 and 8385) constitutes the refereed proceedings of the 10th International Conference of Parallel Processing and Applied Mathematics, PPAM 2013, held in Warsaw, Poland, in September 2013. The 143 revised full papers presented in both volumes were carefully reviewed and selected from numerous submissions. The papers cover important fields of parallel/distributed/cloud computing and applied mathematics, such as numerical algorithms and parallel scientific computing; parallel non-numerical algorithms; tools and environments for parallel/distributed/cloud computing; applications of parallel computing; applied mathematics, evolutionary computing and metaheuristics.
Parallel Programming for Modern High Performance Computing Systems
by Pawel CzarnulIn view of the growing presence and popularity of multicore and manycore processors, accelerators, and coprocessors, as well as clusters using such computing devices, the development of efficient parallel applications has become a key challenge to be able to exploit the performance of such systems. This book covers the scope of parallel programming for modern high performance computing systems. It first discusses selected and popular state-of-the-art computing devices and systems available today, These include multicore CPUs, manycore (co)processors, such as Intel Xeon Phi, accelerators, such as GPUs, and clusters, as well as programming models supported on these platforms. It next introduces parallelization through important programming paradigms, such as master-slave, geometric Single Program Multiple Data (SPMD) and divide-and-conquer. The practical and useful elements of the most popular and important APIs for programming parallel HPC systems are discussed, including MPI, OpenMP, Pthreads, CUDA, OpenCL, and OpenACC. It also demonstrates, through selected code listings, how selected APIs can be used to implement important programming paradigms. Furthermore, it shows how the codes can be compiled and executed in a Linux environment. The book also presents hybrid codes that integrate selected APIs for potentially multi-level parallelization and utilization of heterogeneous resources, and it shows how to use modern elements of these APIs. Selected optimization techniques are also included, such as overlapping communication and computations implemented using various APIs. Features: Discusses the popular and currently available computing devices and cluster systems Includes typical paradigms used in parallel programs Explores popular APIs for programming parallel applications Provides code templates that can be used for implementation of paradigms Provides hybrid code examples allowing multi-level parallelization Covers the optimization of parallel programs
Parallel Programming with Co-arrays (Chapman & Hall/CRC Computational Science)
by Robert NumrichParallel Programming with Co-Arrays describes the basic techniques used to design parallel algorithms for high-performance, scientific computing. It is intended for upper-level undergraduate students and graduate students who need to develop parallel codes with little or no previous introduction to parallel computing. It is also intended as a reference manual for researchers active in the field of scientific computing. All the algorithms in the book are based on partition operators. These operators provide a unifying principle that fits seemingly disparate techniques into an overall framework for algorithm design. The book uses the co-array programming model to illustrate how to write code for concrete examples, but it emphasizes that the important concepts for algorithm design are independent of the programming model. With these concepts in mind, the reader can write algorithms in different programming models based on personal taste and comfort.
Parallele Programmierung
by Gudula Rünger Thomas RauberMultiprozessor-Desktoprechner, Cluster von PCs und Innovationen wie Hyperthreading oder Multicore-Prozessoren machen parallele Rechenressourcen allgegenwärtig. Die Ausnutzung dieser Rechenleistung ist jedoch nur durch parallele Programmiertechniken möglich. Das Buch stellt diese Techniken für herkömmliche Parallelrechner und für neuartige Plattformen umfassend dar. Neben den Grundlagen der parallelen Programmierung werden Programmierumgebungen wie Pthreads, Java-Threads, OpenMP, MPI oder PVM sowie die zugehörigen Programmiermodelle behandelt.
Parallelism in Matrix Computations
by Efstratios Gallopoulos Bernard Philippe Ahmed H. SamehThis book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing a few of the extreme singular triplets. Part IV focuses on the development of parallel algorithms for matrix functions and special characteristics such as the matrix pseudospectrum and the determinant. The book also reviews the theoretical and practical background necessary when designing these algorithms and includes an extensive bibliography that will be useful to researchers and students alike. The book brings together many existing algorithms for the fundamental matrix computations that have a proven track record of efficient implementation in terms of data locality and data transfer on state-of-the-art systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness.